Carlos U. Häubi Segura, PhDdrhaubi@yahoo.com

Physics, Chemistry and Biology of

WATERThe Tenth Annual Water Conference

Bulgaria, October 1-4. 2015

Homeopathy

Memory of water

Messages from water

Bulk water vs.

structured water vs. EZ

Energy from light?

Chronic dehydration

And what about …pH?

“Discovery is seeing what

everybody else has seen, and

thinking what nobody else has

thought.”

Albert Szent-Györgi

Canadian physiologist

University of Manitoba (1943)

MSc in physics and mathematics (1949)

PhD in biophysics (1951)

Emory University , Physiology (1954)

Brown University , Medical science (1965-1983)

Stewart, P.A. (1981). How to Understand Acid-Base. A Quantitative Acid-Base Primer for Biology and Medicine,Elsevier Nordholland, New York

Stewart, P.A. (1983). Modern quantitative acid-base chemistry. Can J Physiol Pharmacol. 61: 1444-1461

Kellum, John A; Elbers, Paul WG, eds. (2009). Stewart's Textbook of Acid-Base. ISBN 978-1-4092-5470-6

.

http://www.acidbase.org/

http://issuu.com/acidbase/docs/htuab

If the data does not fit the theory, it is time to change

the theory

What makes it acid? What makes it alkaline?

What is biologicaly apt pH?Blood?

Cells?

What is an acid diet? What is an alkaline diet?

What are biological limits?

Acids taste sour

acids change blue litmus to red

their aqueous (water) solutions conduct electricity

react with bases to form salts and water as the only products

evolve hydrogen gas (H2) upon reaction with an active metal, such as alkali metals, alkaline earth metals, zinc, iron, aluminum, forming a salt as the only other product

An acid is a substance which forms H+ ions as the only positive ion in aqueous solution

Bases taste bitter

feel slippery or soapy

bases turn red (acidified) litmus back to blue

their aqueous (water) solutions conduct electricity

react with acids to form salts and water as the only products

An alkali is a substance which forms OH- ions as the only negative ion in aqueous solution. A base is an insoluble hydroxide.

Author A theory of Hydrogen A theory of Oxygen

PARACELSUS

(S.XV)Discovers Hydrogen upon

acting on a metalROBERT BOYLE

(1671)(Pointy corpuscules?)

ANTOINE LAVOISIER

(1777)Oxy = acidAll acids contain “O”

HUMPHREY DAVY

(1800)Not all acids contain “O”Hydracids (HCl, HF, HI)“H” = Principle of

acidificationJ.P. DULONG

(1820)Union of an electronegative

compound (Oxygen, halogen) with an electropositivo compound (H) and this can besubstituted by a metal

J.J. BERZELIUS

(1830)Oxides of metaloides

produce acids in waterOxygen = Sauerstoff

(German for “acid substance”)JUSTUS VON LIEBIG

(1838)An acid contains a H-atom

which can be subtituted by a metal

GRAHAM

(1880)Monobasic and polibasic

acids: H is subsituted by a base

Arrhenius (1887)◦ An acid is a substance which forms H+ ions as the only positive ion in

aqueous solution.

◦ An alkali is a substance which forms OH- ions as the only negative ion in aqueous solution. A base is an insoluble hydroxide

Brønsted-Lowry (1923)◦ An acid is a proton donor.

A base is a proton acceptor.

Lewis (1923)

◦ An acid is an electron acceptor,and a base is an electron donor.

◦ This totally removes the concept of hydrogen ions being a pre-requisite for an acid. But like the Brønsted-Lowry definiton above, it still includes every acid and base under the Arrhenius definition, and all those under the Brønsted-Lowry definition.

HCl(g) + NH3(g) ---> NH4Cl(s)

2HCl + MgO ---> MgCl2 + H2O

Zn(OH)2 + 2NaOH(aq) ---> 2Na+(aq) + [Zn(OH)4]2-

(aq)

HCl ---> H+ + Cl-

Water is an acid or a base?

Bicarbonate is a base or an acid?

Where does HCO3- come from?

From NaHCO3

Where does the OH- come from?

From NaOH

H2CO3 is an acid or a conjugated

acid?

Classical theories of acids

◦ Theory of dissociation, Arrhenius-Ostwaldt (1887)

◦ pH scale (pH = -log [H+]), Sørenson (1909)

◦ Henderson-Hasselbalch equation (1916)

◦ Proton donors, Brønsted-Lowry (1923)

◦ Electron donars, Lewis acids (1923)

General definitions of solvents

◦ Effects of solutes on the solvent (Germann, 1925)

◦ Quantitative theory of acids (Stewart,1981)

Concepts of acids in Medicine

◦ Dissociation of strong acids and bases

◦ Partial pressure of CO2 (PCO2)

◦ Buffers

◦ Henderson-Hasselbalch – only one variable

Iatrogenic?

Any new theories?

Old theories are

still actual?

Qualitative or

Quantitative?

Water is really weird...

◦ It forms a permanent dipole

◦ It hydrates other molecules, even other

molecules of water

◦ It forms liquid crystals with moving electric

charges

It dissociates with difficulty (Kd) but re-

associates rapidly (Ka) :

◦ It is the main donador and receptor of hydrogen

ions (= protons: H+) and hydroxile ions (OH-)

◦ Protons (H+) cannot live freely; they associate

and hydrate : H3O+(H2O)n

◦ Water has a high concentration of H2O: 55.5 M

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

H

HOd-d+

HO

H

H3O

+

H3O+

HO

H

H

O

HH

HO

H

O H +

H +104.5°

Protonicjumps

----

One molecule in each 10 million dissociates

spontaneously:

◦ 0.1 ppm , 1/107 , 10-7 (pH=7)

The reaction is the following:

H2O H+ + OH- H+ + H2O H3O+

The proton binds to another molecule of water

O -

H +

H +

O -

H +

H +

O -

H +

H +

O -H + O -

H +

H +

H +

H3O+

H +

O -H + OH-

Theory of dissociation, Arrhenius-Ostwaldt

(1887)

How is this possible?

General definitions of solvents

H3O+

O -

H +

C

H +

H +

H +

CO -

O -

H +

H2OÁcido no-disociado:

No tiene carga

Ácido disociado:

Carga (-) = anión

O -

H +

H +

O -

H +

H +

O -

H +

O -

H +

H +

H +

O - Ac

O -

H +

O -

H +

H +H +

H +

H +H +

Cristal de agua tiene carga

neutra

Matriz de agua:

Donador y receptor

de protones

y iones OH-

Saltos protónicos

Dónde quedó la bolita?

H +O -

H +

H +

Acido orgánico se protoliza:

se forma un anión solvatadoPor cada carga negativa se

genera un protón H+

El protón no tiene vida

libre, se forma el ion

hidrogenion H3O+

The neutral charge

in water is always

maintained

According to Germann (1925)

◦ Cation of water (H3O+): “Lyonium”

◦ Anion of water (OH-): “Lyate”

For a given solvent:

◦ Acid: a substance that increments the concentration of the “Lyonium” ion

and reduces the concentration of the “Lyate” ion

◦ Base: a substance that increases the concentration of the “Lyate” ion and

decreases the concentration of “Lyonium” ion.

In the case of water, acids and bases can be defined as :

◦ Acid: A negative charge that produces a mayor dissociation of water and

an increase in the concentration of protons, [H+]

◦ Base: A positive charge that produces a mayor dissociation of water

molecules and an increase in the concentration of hydroxile ions, [OH-]

Strong Ion Difference

PCO2=

ATOT=

pH

[H+]

[OH-]

[HCO3

-]

[CO3

2-]

[A-][HA]

Variables dependientes

PresiуnParcial deCO2 Total de

anionesdйbiles

SID=

Seis ecuacionessimultбneas

Henderson-HasselbalchpH = pKa + Log [A-]/[HA] ?

Aniones dйbiles

Cationesfuertes

PCO2

Anionesfuertes

Na+

Cl-

K+

Ca2+

Mg2+

OH- H3O

+HCO3

-

CO3

2-

A-

HA

SO4

2-

??

?

?

?

Dissociation of strong acids and bases

Partial pressure of CO2 – PCO2

Dissociation of weak acids

SID – Strong Ion Difference

Partial pressure of CO2 – PCO2

ATOT – Total of weak anions

Three factors that affect pH but could not be reconciled...

now braught together by a quantitative method

Strong Ion Difference:

Na + K + Ca +Mg

-Cl – strong ions

= SID

pCO2:

Protein concentration Atot]

Chemistry laws:

- Mass action:

- Electro-neutrality:

- Dissociation of: water, carbonic acid,

weak acids, weak bases, ammonia, etc.

[H+] [OH-] [HCO3-] [CO3

2-] [A-] [Pi] [VFAs] [Lactates]

Phosphates, ammonia, etc.

Weak acids: VFA Lactate

Stewarts theory is based on the effect of three

basic principles of chemistry, on the balance

of electrical charges in aqueous solutions:

1) Principle of electro-neutrality,

2) Law of Mass Action,

3) Law of Mass Conservation

1) Principle of electro-neutrality

the sum of all positive charged ions must equal the sum of allthe negatively charged ions:

[Na+] + [K+] + [Ca2+] + [Mg2+] + [H+] - [Cl-] –

[Anion-]-[OH-] - [HCO3-] - [CO3

2-] = 0

0

20

40

60

80

100

120

140

160

Cationes Aniones

mm

ol/L

OH-

Pi

Atot

HCO3-

Otros Aniones

Cl-

H+

Ca2+

K+

Na+

2) Law of Mass Action

States that all incompletely dissociated substances reach a dissociation equilibrium:

[A] * [B] = K * [C]

where K is the rate constant for the reaction.

Water has a very small dissociation constant:

KW (KW = 1*10-14)

but a very large association constant:

(1/KW = 1*1014)

3) Law of Mass Conservation

States that the amount of a substance remains constantunless it is added, removed, generated or destroyed:

[HA] + [A-] = [ATOT]

The total of a weak acid (ATOT) is an independent variable

and can be present as a dissociated acid (A-)

or non-dissociated (HA),

both being dependent variables.

The dissociation of water into H+ ions (pH) and OH- and thebehavior of other weak acids (organic acids, carbonates,phosphates and proteins) and bases (ammonia), dependson three independent variables:

1) The Strong Ion Difference (SID)

Na+ + K+ + Ca2+ + Mg2+ - Cl- - SO42-

2) The partial pressure of carbon dioxide (PCO2)

CO2 + H2O H2CO3 H+ + HCO3- 2 H+ + CO3

2-

3) The total amount of weak anions (ATOT)

HAlb + Alb- = AlbTOT

Water is the primary and inexhaustible source and sink for

hydrogen ions.

[H2O]* KW = [H+] * [OH-]

The dissociation constant KW is very small

( 4.3 * 10-16Eq/l at 37 oC).

KW varies with temperature

(e.g., at 25 °C, KW is about 1.8 * 10-16Eq/l)

The approximate value of KW' is:

KW' = 8.754 * 10-10 * e(-1.0^1*10^6) / T^2)

where temperature T is expressed in degrees Kelvin

This can be done with the solution of six simultaneous

equations:

[H+] * [OH-] = KW‘ Equation #0

[H+] * [A-] = KA * [HA] Equation #4

[HA] + [A-] = [ATOT] Equation #5

[H+] * [HCO3-] = KC * PCO2 Equation #8

[H+] * [CO32-] = K3 * [HCO3

-] Equation #9

and finally, to maintain electrical neutrality:

[SID] + [H+] - [HCO3-] - [A-] - [CO3

2-] - [OH-] = 0

Equation #10

This makes the solution for the hydrogen ion concentration[H+] possible with the aid of computers:

[SID] + [H+] - KC * PC / [H+] - KA * [ATOT] / (KA + [H+]) – K3 *

KCPC / [H+]2 - KW' / [H+] = 0

Equation #10

PC = PCO2 mmHg

Constants are:

KW = 4.40*10-14 (Eq/L)

KC = 2.34 * 10-11 (Eq/L)2 mmHg-1

K3 = 6.0*10-11 Eq/L

KA = 1.64*10-7 Eq/L (rest)

KA = 1.98*10-7 Eq/L (exercise)

KC = K * S◦ where K = 7.42*10-7 Eq/L, K is the constante of dissolution;

◦ S = 0.0351 Eq/L mmHg-1 a 37°C y 300 mOsm, S is the constant of Solubility.

The algebra to solve these six simultaneous equations gives

a fourth-order polynomial.

The exact solution for [H+] is:

[H+]4 + ([SID] + KA) x [H+]3 +

(KA x ([SID] – [ATOT]) – K’W – KC x PCO2) x [H+]2

- (KA x (K’W + KC x KCO2) – K3 x KC x PCO2) x [H+] – KA x K3

x KC x PCO2 = 0

There are four possible solutions

PROGRAM STARTS:

◦ TOO_SMALL = 4.4 * 10-14

◦ TOO_BIG = 1.0

◦ CLOSE_ENOUGH = 0.000001

BEGIN:

◦ MY_GUESS = ROOT ( TOO_SMALL * TOO_BIG )

◦ RESULT = F(MY_GUESS)

◦ IF ABS(RESULT) LESS THAN CLOSE_ENOUGH THEN RETURN MY_GUESS

◦ IF RESULT IS POSITIVE THEN

TOO_BIG = MY_GUESS

OTHERWISE

TOO_SMALL = MY_GUESS

GO TO BEGIN

PROGRAM ENDS:

Written by J. van Schalkwyk, 1999, from the website:

http://www.anaesthetist.com/icu/elec/ionz/Stewart.htm

University of South Carolina, School of Medicine

http://ppn.med.sc.edu/watson/Acidbase/Acidbase.htm

No free-living protons (H+):

The acidity of the bicarbonate ion

The volatility of the bicarbonate ions

The effect of acids on EZ-water

Let’s start with this one!

Fig. 5.9 Time course of pH-dye distribution

as current flows between wire electrodes

immersed in a water bath containing pH-

sensitive dye.

Cathode (-):

◦ Purple corresponds to high pH

◦ Attracts cations (+), Produces OH-

Anode (+):

◦ Orange corresponds to low pH

◦ Attracts anions (-), Produces H+, H3O+

low pHhigh pH

Initial state

Fig. 5.5 Addition of microspheres alters water’s pH.

(a) Carboxylate microspheres, 1 μm diameter.

Increasing microsphere concentration changes dye color

toward red, indicating lower pH.

(b) Positively charged amino microspheres change dye

color toward green, indicating higher pH.

Does Stewart help explain EZ

after formation or depletion?

Pollack (2013):

“an H3O+ combining with a

lattice-structural unit (OH-),

which yields two water

molecules (Fig. 6.11). This

erosive action loosens the

EZ’s hexameric structure.”

Sufficiently acidic pH does diminish EZ size.

Salts erode the EZ similarly.

Consider NaCl:

The Cl– component can combine with H3O+ in

the bulk to yield HCl + H2O,

Na+ can invade the negative lattice, and go on to

create NaOH by extracting a lattice OH– unit.

The EZ erodes and adds a water molecule to the

bulk water. Wherever the lattice is open, positive

ions of any sort can enter and cause EZ erosion.

According to Stewart:

• Cl- increases [H+], therefore [H3O+]

• Na+ ion reduces [H+] and increases [OH-]

• Question to Jerry: Effect of NaOH on EZ?

“an H3O+ combining with a lattice-

structural unit (OH-), which yields two

water molecules (Fig. 6.11). This erosive

action loosens the EZ’s hexameric

structure.”

The no free-living existence of protons (H+):

◦ Protons disociate and re-associate from the water

matrix in order to maintain the principle of

electroneutrality

◦ Hydrogen ions H+ have a diameter of 10-15m, therefore

cannot be pumped by membrane proteins

◦ Hydrogen ions H+ are dependent variables

◦ Mitchell’s Chemiosmotic Hypothesis (1961) cannot be

correct (ATP is formed through another mechanism!)

http://bcs.whfreeman.com/thelifewire/content/chp07/f07012.gif

The acidity of the bicarbonate ion

◦ The bicarbonate ion is not a buffer… it cannot

neutralize acidity in a solution

◦ CO2(d)+ H2O H2CO3 H++ HCO3-H++H+ + CO3

2

◦ It’s an anion (HCO3-), a negative charge, pKa 6.1: it’s a

weak acid

◦ What increases pH is the cation (e.g. Na+, K+)

◦ Henderson-Hasselbalch equation is wrong !!

H-H (1916)

◦ pH = pKa + log [A-] /[HA]

◦ It’s a circular relationship:

pH affects the dissociation of carbonic acid into bicarbonate

The dissociation of carbonic acid affects the concentration of bicarbonate and carbonic acid

Anion Gap◦ (Na+ + K+) - (Cl- + HCO3

-) = UA –UC

◦ Value: 10-12 mEq/L

Base Excess◦ Van Slyke equation:

◦ PaCO2 40 mmHg, pH 7.4, 37 °C, full O2 saturation)

◦ Base excess = 0.93 × HCO3− − 24.4 + 14.8 × (pH − 7.4)

◦ SBE = 0.9287 × (HCO3- − 24.4 + 14.83 × ([pH − 7.4]))

pH = 6.1 + log10 [HCO3− ]

0.03 × PaCO2

Winter’s equation:

PCO2 = 1.54 × [HCO3- ] + 8 ± 2

Ole Siggard-Andersen Nomogram

The volatility of bicarbonate ions

◦ Bicarbonate ions are dependent variables, which are formed

or destroyed according to the Henderson reaction:

CO2(d)+ H2O H2CO3 H++ HCO3-H++H+ + CO3

2

◦ Carbonic Anhidrase, a really fast enzyme

◦ There is NO evolutionary advantage of pumping HCO3- ions

from one side of a membrane to the other, because it will be

change to another species of carbonate according to

conditions of the medium

The volatility of bicarbonate ions (continues):

◦ There is no reabsorption of bicarbonate in the kidneys

during urine production

◦ NO interchange of HCO3- ions for Cl- ions during gastric

juice production

◦ NO secretion of HCO3- ions during pancreatic juice

production

◦ NO use of applying bicarbonate in IV-solutions – it’s the

sodium ion (Na+HCO3-)

Lumen Cell Blood

Cl-

No c.a.

c.a. = carbonic anhidrase

met

aboli

zed

Ac- Ac

-

HAc HAc

H+

H++

Na+

CO2

H2O

H2CO

3

HCO3

-

H+

+

+

c.a.CO

2H

2O

H2CO

3

HCO3

-

H+

+

+

Ac-

CO2

H2O

H2CO

3

HCO3

-

H+

+

+

c.a.

A hypothetical model of rumen epithelial ion transport (adapted from Stevens, 1988).

Lumen Cell Blood

No c.a.

met

abol

ized

Ac- Ac

-

HAc HAc

H+

H++

CO2

H2O

H2CO

3

HCO3

-H

+

+

+

Ac-

Strong ions (e.g. NaCl) completely dissociate in water and are hydrated by water molecules releasing

an opposite charged water ion (H30

+ or OH

-) to maintain electroneutrality in the aqueous solution.

Carbon dioxide (CO2) dissolved in water reacts to forms different species of carbonate according to

other variables in the medium.

Weak acids (HAc) dissociate into their anions (Ac-) according to their dissociation constant (Ka).

(H30

+ = H

+); c.a. = carbonic anhidrase.

H2ONa

+

H2OCl

-+ H

++

+ OH-

+

Cl-

Na+

NaCl

CO3

2-H

++

HAc

H2O

OH-

H2O

Pool

H+

H+

H+

H+

KaKa Ka

H2O

OH-

H2O

Pool

H+

H+

H+

OH-

OH-

H+

H+

Cl-

Na+ Na

+

Cl-

H+

+

Fermentation

OH-+

H++

CO2

H2O

H2CO

3

HCO3

-H

+

+

+

c.a.

CO3

2-H

++

CO2

H2O

H2CO

3

HCO3

-H

+

+

+

c.a.

CO3

2-H

++

Definition:

◦ The administration of fluids and electrolytes with the

objective of maintaing or restablishing corporal

homeostasis

Priorities:

◦ To conserve the volume of blood

◦ To conserve osmotic pressure and equilibrate ion

composition in each body compartment

◦ To conserve normal concentration of hydrogen ions (pH) in

each compartment

Author(s), year Research Solution used Observations

Denys, 1667 First blood transfusion From a dog to a human RIP

O’Shaughnessy, 1831 Loss of water, alcali and salts in blood in cases ofcholera

Pérdida de agua, álcali libre, urea en orina, bajo en carbonato de sodio

Not known if it was 0.9 % NaCl

Latta, 1832 Loss of soidum volumein an elderly woman

Use of glass tube intobasilic vein, 3.4 L

“Rapid recovery butdied because treatmentwas not followed”

Stadelman, 1883 Acidosis in diabeticcoma

Alcaline Sol.: Na2CO3: 2-3 %

2 % = 208 mM3 % = 312.5 mM

Ringer, 1882 Frog’s heart can survivein a balanced solution

1 Litre contains: Sodium chlorine (6.5 g), Sodium bicarbonate (0.2 g) Calcium chlorine(0.25 g) y Potassiumchlorine (0.42 g)

NaCl: 111.2 mEq/LNaHCO3: 3.125 mEq/LKCl: 5.63 mEq/LCaCl2: 2.25 mEq/L

Hamburger, 1882 Establishes thephysiological salinesolution

0.9 % NaCl Mistake: 154 mEq/L !NaCl is only 0.6 %Other salts of Na+ 0.3%

Cantani, 1892 Comatose patients Subcutaneoussolutions: Typhic reactions – RIP!

0.4 % NaCl = 68.44 mM0.3 % Na2CO3 = 31.25 mM

Author(s), Year Research Solutions used Observations

Hartwell & Houget, 1912

Perros: estudio sobre muerte de perros con obstrucción intestinal no estrangulada

Gran pérdida de líquidos por vómito excesivo, administración SC con SSF

SSF puede provocar más vómito, por sobrecarga de cloruro

Rowntree, 1922Produce intoxicación por agua experimentalmente

Descripción del trastorno en el ser humano

Dilución de iones puede llevar a la muerte

Mata, 1924Goteo IV, en vez de goteo rectal y epidermoclisis

Cánula de vidrioMayor velocidad de infusión, pero no da tiempo a que el organismo regule

Hartmann, 1935 Lactantes con diarrea severa

Requieren más sodio que cloruroRinger con LactatoIncluye Calcio, potasio

Na+ : 131 mmol/LCl- : 111 mmol/LLac-: 29 mmol/LK+ : 5 mmol/LCa2+: 2 mmol/L

Darrow & Yannet, 1935Movimiento de liquido entre compartimentos, sin radioisotopos

Diagrama Darrow- Yannet

Gamble, 1942Movimiento de liquido entre compartimentos

Gamblegrama Diagrama muy útil

Darrow, 1949Pediatría,Diarrea severa

35 mEq/L de KClSe recomienda en casos de acidosis por pérdida de potasio, pero contiene alto cloruro y lactato

Na+ .: 121 mmol/LCl- : 103 mmol/LLac-: 53 mmol/LK+ : 35 mmol/L

Fogelman & Wilson, 1960Perros, hombresTraumatismo severo

Pérdida de liq. Extracelular, reposición con sal.

Solutions Na+ K+ Ca2+ Cl- Precursors SID pH*

SSF

0.9% NaCl

154 0 0 154 0 0 7.30

Ketone-R 131 5 3 111 +28 ßOH-Butirate

+25.5 7.38

Ringer

DL-Lactate

131 5 3 111 +28DL-Lactate +25.5 7.38

Ringer

L-Lactate

131 5 3 111 +28 L-Lactate +25.5 7.38

Glucosa 5% + 0.9% NaCl

154 0 0 154 + 5 % Glucose

(560 mOsm)

0 7.30

Plasma

Stewart

143 4 3 107

+ 1

+25.1 HCO3- +42 7.42

McSherry 138 12 3 100 +50 Acetate +54.5

+41

7.45

7.42

PlasmaLyteA

140 5 0

Mg2+ 3

98 + 27 Acetate

+ 23 Gluconate

+40 7.40**

*pH: calculated as the result of adding 1 L solution to a patient with 5 L of blood:

pH 7.41 , PaCO2 40mmHg, Albumin 19mEq/L.

** published values

Plasma cationes

Plasma aniones

Intersticial cationes

Intersticial aniones

Intracelular cationes

Intracelular aniones

Proteínas citoesqueleto 0 0 50

Proteínas solubles 16 0 55

Ácidos orgánicos 3 4 3

SO42- 0.5 0.5 10

PO43- 1 1 57

HCO3- 26 30 8

Cl- 102 114 2

Mg2+ 1 0.5 13

Ca2+ 2.5 2.5 1.5

K+ 4 4 160

Na+ 142 144 10

0

20

40

60

80

100

120

140

160

180

200

Ion

co

ncn

etr

ati

on

(m

Mo

l/L

)

Plasma (g/dL)

Urine(g/dL)

Plasma (mmol/L)

Urine(mmol/L)

Diff. Conc.

Reabs. %

Water 90-93 95 52M 53M - 99.1

Protein 7.0-8.5 - 1.3 -

Urea 0.03 2 5 333 X 60 41.4

Uric acid 0.002 0.03 X 15

Glucose 0.1 - 5.5 - 100

Creatinine 0.001 0.1 X 100

Sodium 0.32 0.6 140 188 X 2 99.1

Potasium 0.02 0.15 5 38 X 7

Calcium 0.01 0.015 2.5 3.8 X 1.5 98.8

Magnesium 0.0025 0.01 1 4 X 4

Chlorine 0.37 0.6 105 171 X 2 98.5

Phosphates 0.003 0.12 0.32 12.6 X 40

Sulfates 0.003 0.18 0.31 18.75 X 60 76.5

Ammonia 0.0001 0.05 0.06 29.4 X 500 20.5

Plasma (mmol/L)

Urine

(mmol/L)

Urine+NH4+

(mmol/L)

Sodium 140 188 188

Potasium 5 38 38

Calcium 2.5 3.8 3.8

Magnesium 1 4 4

Chlorine 105 171 171

Phosphatos 1.4 12.6 12.6

Sulfates 0.31 18.75 18.75

Cations +148.5 +234 +234

Anions -106.7 -203 -203

SID’ +41.8 -31 -31

Other Cations 0.06 - 38 (29 NH4+)

SID” +42 -31 +7

pH-calc 7.4 1.4 5.6

Variables Normal ↑Anion- ↓Na+ SO42- ↑PaCO2 ↑PaCO2

↓ ATOT

Na+ 140 140 131 140 140 131 131

K+ 4 4 4 4 4 4 4

Ca2+ 4 4 4 4 4 4 4

Cl- 104 104 110 104 104 104 104

Otros- 6 16 6 6 6 6 6

SO42- 0.6 0.6 0.6 7.0 7.0 7.0 7.0

SID 38 32 23 31 31 22 31

PaCO2 40 40 40 40 50 50 50

Alb- 4.2 4.2 4.2 4.2 4.2 4.2 2.1

Pi- 1.4 1.4 1.4 1.4 1.4 1.4 1.4

HCO3- 24.0 18.5 10.8 17.6 18.1 10.5 23

CO2tot 25.3 19.8 12.0 18.9 19.6 12.0 24.5

BE -0.65 -6.65 -15.65 -7.65 -7.65 -16.65 -1.96

AG 12.0 11.6 10.2 18.4 17.9 16.5 13.0

pH 7.39 7.28 7.04 7.25 7.17 6.93 7.27

Traditional theories of acids Stewart’s theory (1981)

Proton donors

Brønsted-Lowry (1923)

Generalized solvent definitions

(Germann, 1925)

Henderson-Hasselbalch equations (1916)

only one variable

Nomogramas

A system of simultaneous equations with 6

variables

Electroneutral equilibrium of water

Confussion of dependent and independent

variables: H+, HCO3-

Independent variables:

SID, PCO2, ATOT

Dependent variables:

H+, OH-, HCO3- CO3

2-, A- , HA

Anion gap: 10-12 mEq/L Anion gap: 6-8 mEq/L

Applications: Only for small ranges of pH

e.g. Blood pH (7.0-7.8)

Cations: Na+, K+, Ca2+, Mg2+, NH4+

Anions: Cl-, SO42-, PO4

3-, R-COO-

pH PaCO2

Boston School

(Henderson-

Hasselbalch)

Stewart’s

theory

Respiratory

Acidosis

Normal or HCO3-

(compensated)

PaCO2

(dysnea)

Respiratory

Alcalosis

Normal or HCO3-

(small)

PaCO2

(hypervent.)

Metabolic

Acidosis

Anion gap

-Normal:

-Augmented:

Normal or HCO3-

- loss HCO3-

Excr. H+

Prod. HCl

Anions (Lac-)

H+ + HCO3-

They do not

affect!

Cations

Anions

Metabolic

Alcalosis

Normal or

(small)

HCO3-

Anions

Cations

Electrochemical acidosis

Analysis of clinical cases in ICU

Cálculo de pH y otros iones según Stewart

-

10

20

30

40

50

60

70

80

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7

Tiempo (8am a 7am)

Co

nce

ntr

ació

n (

mm

ol/L

)

7.0

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

SIDcambio

PCO2

Atot

pH

H+

OH-

HCO3

CO32-

A-

HA

PO4

Acidez H+ nanoEq/L

pHcalc

pHpaciente

Pacient with HyponatremiaTiempo pH Na+ K+ Ca2+ Mg2+ Cl- SO42-Lactato-PO43- SID pCO2 ATOT pHcalc

1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

4 7.2 131 4 2 1 105 3 1 2 29 40 19 7.209

5 7 124 4 2 1 105 3 1 2 22 40 19 7.009

6 7 124 4 2 1 105 3 1 2 22 40 19 7.009

7 7.05 126 4 2 1 105 3 1 2 24 40 19 7.074

8 7.1 127 4 2 1 105 3 1 2 25 40 19 7.104

9 7.2 131 4 2 1 105 3 1 2 29 40 19 7.209

10 7.3 135 4 2 1 105 3 1 2 33 40 19 7.297

11 7.35 138 4 2 1 105 3 1 2 36 40 19 7.354

12 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

13 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

14 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

15 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

0

20

40

60

80

100

120

140

160

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6.8

6.9

7

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

Na+

K+

Ca2+

Mg2+

Cl-

SO42-

Lactato-

PO43-

SID

pCO2

ATOT

pH

pHcalc

Pacient with lactic acidosisTiempo pH3 Na+ K+ Ca2+ Mg2+ Cl- SO42-Lactato-PO43- SID pCO2 ATOT pHcalc

1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

4 7.2 140 4 2 1 105 3 11 2 28 40 19 7.209

5 7 140 4 2 1 105 3 20 2 19 40 19 7.04

6 7 140 4 2 1 105 3 20 2 19 40 19 7.04

7 7.05 140 4 2 1 105 3 19 2 20 40 19 7.07

8 7.1 140 4 2 1 105 3 18 2 21 40 19 7.103

9 7.2 140 4 2 1 105 3 14 2 25 40 19 7.209

10 7.3 140 4 2 1 105 3 10 2 29 40 19 7.297

11 7.35 140 4 2 1 105 3 7 2 32 40 19 7.354

12 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406

13 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406

14 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406

15 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406

0

20

40

60

80

100

120

140

160

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6.8

6.9

7

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8Na+

K+

Ca2+

Mg2+

Cl-

SO42-

Lactato-

PO43-

SID

pCO2

ATOT

pH3

pHcalc

Pacient with respiratory acidosis

0

20

40

60

80

100

120

140

160

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6.8

6.9

7

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8Na+

K+

Ca2+

Mg2+

Cl-

SO42-

Lactato-

PO43-

SID

pCO2

ATOT

pH

pHcalc

Tiempo pH Na+ K+ Ca2+ Mg2+ Cl- SO42-

Lactat

o- PO43- SID pCO2 ATOT pHcalc

1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

4 7.2 140 4 2 1 105 3 1 2 38 64 19 7.201

5 7 140 4 2 1 105 3 1 2 38 106 19 7.001

6 7 140 4 2 1 105 3 1 2 38 106 19 7.001

7 7.05 140 4 2 1 105 3 1 2 38 93 19 7.053

8 7.1 140 4 2 1 105 3 1 2 38 82 19 7.102

9 7.2 140 4 2 1 105 3 1 2 38 64 19 7.201

10 7.3 140 4 2 1 105 3 1 2 38 50 19 7.299

11 7.35 140 4 2 1 105 3 1 2 38 44 19 7.351

12 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

13 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

14 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

15 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

Stewart, P.A. (1981). How to Understand Acid-Base. A Quantitative Acid-Base

Primer for Biology and Medicine, Elsevier Nordholland, New York.

Stewart, P.A. (1983). Modern quantitative acid-base chemistry. Can J Physiol

Pharmacol. 61: 1444-1461.

Häubi Segura, C.U. (2004). Use of the Rumen Simulation Technique (RUSITEC)

to model clinical and subclinical rumen acidosis in dairy cattle. PhD Thesis,

Department of Agriculture, The University of Reading, Reading, UK.

From the above we know that

[H+] * [OH-] = KW'

To determine the hydrogen ion concentration it is necessary

to know KW', and the other variable, the hydroxyl ion

concentration. In pure water the only ions present are

hydrogen ion and hydroxyl ion, so if the water is to be

electrically neutral, then:

[H+] - [OH-] = 0

The dissociation of water into hydrogen ions responds to

the chemical laws to maintain electro-neutrality. An

excess of other positively charged ions will decrease the

dissociation of water into H+ ions, conversely, an excess

of negatively charged ions increase the dissociation of H+

ions.

With the addition of strong electrolytes to water, such as

NaOH and HCl, which will almost completely dissociate,

there is a mix of water, Na+, Cl-, H+ and OH- ions.

[H+] - [OH-] + [Na+] - [Cl-] = 0 .. Equation #1

If the amount of sodium and chloride ion (or any other

strong ions) in solution is known, it is possible to

determine the hydrogen ion concentration. Only the

difference in ionic concentrations (SID) is of importance,

therefore the above equation can be abbreviated to:

[SID] + [H+] - [OH-] = 0

A weak acid, HA (such as albumin or VFAs) dissociates to form

H+ and A-, as follows:

HA <=> H+ + A-

Previous equations (dissociation of water and the requirement

for electrical neutrality ) are slightly modified to include the

dissociated anion A-, derived from the acid:

[H+] * [OH-] = KW' Equation #0

[H+] + [OH-] + [SID] + [A-] = 0 Equation #1A

The following two equations are based on the dissociation of

the acid, and the necessity for conservation of the total

amount of acid, which is abbreviated to ATOT :

[H+] * [A-] = KA * [HA] Equation #4

[HA] + [A-] = [ATOT] Equation #5

The effect of carbon dioxide on aqueous solutions is

generally expressed by the Henderson-Hasselbalch

equation, but this only represents part of the truth.

Four reactions can happen to CO2 gas when exposed to

water:

1) Dissolution in water,

2) Reaction with water to from carbonic acid,

3) Dissociation to form bicarbonate ion,

4) Second dissociation to form carbonate ions:

CO2(d) + H2O K1 H2CO3 K2 H+ +

HCO3- K3 H+ + H+ + CO3

2-

The two most significant reactions are the formation of

carbonate and bicarbonate, as each has its own equilibrium

constant. These reactions with their equilibrium constants

will have a profound influence on the whole system, but it is

only in the context of the whole system that is possible to

understand the role of carbon dioxide:

1. CO2 can dissolve in water, as expressed by the equation:

CO2(gas) <=> CO2 (dissolved)

The forward reaction depends on partial pressure of CO2,, =

with a rate

Kf * PCO2

The reverse reaction depends on the concentration of dissolved

CO2 with the rate

Kr * [CO2 (dissolved)]

According to Henry´s Law, the dissolution of molecular

carbon dioxide [ CO2(dissolved) ] into the rumen fluid

medium is related to the solubility coefficient for carbon

dioxide (SCO2) and the partial pressure of carbon dioxide

(PCO2) via the formula:

[CO2(dissolved)] = SCO2 * PCO2 Equation #7A

The solubility of CO2 (SCO2) has substituted Kf/Kr .

SCO2 is dependent on temperature, and at 37 °C it is about

3.0 * 10-5 Eq/litre/mmHg.

2. CO2 can react with water to form carbonic acid:

CO2 + H2O H2CO3

Equilibrium is represented by:

[CO2(dissolved)] * [H20] = K * [H2CO3] .. Equation #7B

If [H20] is treated as a constant, it can be rearranged:

[H2CO3] = KH * PCO2

The value of KH at 37 °C is 9 * 10-8 Eq/litre - therefore, the

H2CO3 concentration is far smaller than the amount of

dissolved CO2.

The reaction of CO2 with water is very slow , with a half time

of about 30 seconds, speeded up to microseconds by the

carbonic anhydrase abundantly present in most tissues

but not in the rumen.

3. H2CO3 thus formed can dissociate into bicarbonate and

hydrogen ions:

H2CO3 H+ + HCO3-

Equilibrium is represented by:

[H+] * [HCO3-] = K * [H2CO3]

It follows that:

[H+] * [HCO3-] = KC * PCO2 Equation #8

A physiological value for KC is

2.6 * 10-11 (Eq/l)2/mmHg

4. Once formed, HCO3- can rapidly dissociate:

HCO3- H+ + CO3

2-

Equilibrium is represented by:

[H+] * [CO32-] = K3 * [HCO3

-] Equation #9

A typical value for K3 is 6 * 10-11 Eq/litre.

CO2(d) + H2O K1 H2CO3 Kc H+ + HCO3-

K3 H+ + H+ + CO32-

Stewart’s original theory combined strong ions, carbon

dioxide and a weak acid to model blood plasma and

intracellular fluids.

Blood plasma is rich in weak acids, specially proteins

(albumin) and for the purposes of analysis and simplicity

he regarded them as being all one acid with a single ATOT

and single KA.

Nevertheless it is possible to expand the model with

multiple KA (Figge et al., 1991).

Fencl Model:

pH = f(pH){SID, PCO2, [PiTOT ], [Albumin], [CitrateTOT ]}

The knowledge of the independent variables ( [SID], PCO2,

and ATOT) and the equilibrium constants KW', KA, KC and

K3. allow to calculate any one of eight dependent

variables:

◦ HCO3-

◦ A-

◦ HA

◦ CO2 (dissolved)

◦ CO32-

◦ H2CO3

◦ OH-

◦ H+

Note that dissolved CO2 and H2CO3 are easily determined

from Equations #7A and #7B.